1. Let's start with a simple algebraic equation: Solve for $x$ in the equation $$2x + 3 = 11$$. 2. The formula to solve linear equations is to isolate the variable on one side. We do this by performing inverse operations. 3. First, subtract 3 from both sides: $$2x + 3 - 3 = 11 - 3$$ which simplifies to $$2x = 8$$ 4. Next, divide both sides by 2 to solve for $x$: $$\frac{2x}{\cancel{2}} = \frac{8}{\cancel{2}}$$ which simplifies to $$x = 4$$ 5. So, the solution to the equation is $x = 4$. 6. Let's verify by substituting $x=4$ back into the original equation: $$2(4) + 3 = 8 + 3 = 11$$ which is true. This confirms our solution is correct.